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arXiv:quant-ph/0008104 · Journal of the Physical Society of Japan

Dynamical Revivals in Fermi Accelerator

Farhan Saif

Published Aug 15, 2000• 6 citations
arXivHTMLPDF

Abstract

We investigate quantum revivals in the dynamics of an atom in an atomic Fermi accelerator. It is demonstrated that the external driving field influences the revival time significantly. Analytical expressions are presented which are based on semiclassical secular theory. These analytical results explain the dependence of the revival time on the characteristic parameters of the problem quantitatively in a simple way. They are in excellent agreement with numerical results.

DOI
10.1143/jpsj.69.2363

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Quantum revivals in micromasers

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A distinctive signature of the granulated nature of the electromagnetic field is the revivals known to occur in the dynamics of a two-level atom interacting with a single-field mode (Jaynes-Cummings model). The development of high-Q single-mode cavities combined with progress in Rydberg atom spectroscopy has led to a possibility of verifying these predictions. Revival experiments using micromasers have been performed by Walther et al. Here the cavity mode is first allowed to reach a steady state, and then probe atoms are injected into the resonator. By measuring their state as they exit the cavity, one can infer the state of the field. We show that the micromaser experiences Jaynes-Cummingslike revivals when the pump parameter θ is varied. However, in contrast to the conventional Jaynes-Cummings situation, which considers initially coherent fields, the micromaser photon statistics are usually not Poissonian and depend sensitively on θ. The micromaser revivals cannot be explained by a semiclassical theory or linearized quantum fluctuations about the semiclassical solution. Rather, an exact quantum treatment, considering fully the granularity of the cavity mode, is required.

Annual Meeting Optical Society of America•Jan 1, 1988•0 citations
We investigate quantum revivals in the dynamics of an atom in an atomic Fermi accelerator. It is demonstrated that the external driving field influences the revival time significantly. Analytical expressions are presented which are based on semiclassical secular theory. These analytical results explain the dependence of the revival time on the characteristic parameters of the problem quantitatively in a simple way. They are in excellent agreement with numerical results.
Quantum revivals are investigated for the dynamics of an atom in a driven gravitational cavity. It is demonstrated that the external driving field influences the revival time significantly. Analytical expressions are presented which are based on second-order perturbation theory and semiclassical secular theory. These analytical results explain the dependence of the revival time on the characteristic parameters of the problem quantitatively in a simple way. They are in excellent agreement with numerical results.
We study periodically driven one dimensional box in the presence of weak modulating force and provide analytical calculations for time of quantum revivals and explain via spatiotemporal behavior. Presently introduced analysis can be applied to calculate the time of revivals in the system subject to any periodically changing weak external driving force. Spatiotemporal behavior provides the modified numerical values of revival times which have good agreement with our analytical results. Moreover, spatiotemporal evolution shows absence of symmetry beyond a revival time, which contributes to change of slope in subsequent canals and ridges.
The idea of wave packet, that clarified many conceptual difficulties, has more recently been revisited to address interferometric and dynamical issues.Present work focuses on the spatio-temporal dynamics of the quantum wave packets in the Fermi-Ulam Accelerator Model.The specific system considered here is a one-dimensional box under periodic oscillations at one boundary. Such a seemingly simple system can be mapped to non-trivial problems like BEC trapped in an oscillating cavity or dynamics of atomic wave packet in different potential in presence or absence of gravitational field.The system is shown to display rich dynamical features including transitions from regular to stochastic and further to chaotic domain in classical phase space. We have obtained the approximated eigen-value solutions of the problem through time dependent Schrodinger’s equation under rescaling transformations that effectively replace moving boundary with a static one. Consequently the running time becomes a nonlinear function of the continuously changing boundary.Based on these solutions, revivals or the resurrection of the original wave packet, in the driven and un-driven Fermi-Ulam model are presented. Such revivals correspond to the constructive interference whereas the wave packet’s collapse owes to destructive interference. Furthermore, interplay of constructive and destructive interferences also readily mimics the fractional revivals.It is further demonstrated that initial position and momentum play a highly crucial role in the emergent revival and fractional revival patterns.It is shown that the symmetries exhibited by such structures in un-driven systems are usually lost under driven conditions and the revival/fractional revival times can only be predicted through a transcendental equation whose solution mainly depends on the strength of the external driving force.In present thesis we have proposed a comprehensive mathematical technique to calculate these hitherto unpredictable times.In addition, a graphical method is also suggested to observe these asymmetric revival/fractional revival times.This apparent asymmetry, do display an overall periodicity over a comparatively long span covering many times of revivals.It is found that whenever the ratio between the period of wall oscillation and quantum revival time `α/β' is a rational number then the revivals time shows a periodicity after β number of revival times over α wall oscillation. Standard tools of autocorrelation and quantum carpets, a consequence of quantum interference, have been employed for visual manifestation of these revivals.These carpets amply demonstrate the explicit asymmetric shifting of revival times for the driven case.These micro changes exhibited in quantum carpet morphologies consequently yield amended phase velocities associated with the canals and ridges in the driven framework.Furthermore, to grasp the quantum phase space dynamics in its entirety, we have also utilized the more sophisticated techniques of the Wigner function and information entropy.It is demonstrated mathematically that revivals not apparent via autocorrelation become prominent in the Wigner phase space description along with the appearance of smooth mini wave packets in the fractional revivals.These interference patterns emerge due to the state vector formed through the linear combination of Gaussians with different positions and momenta having pure Gaussian as well as oscillatory terms. Moreover, the information entropy, like the Wigner function also predicts the revivals when and where they happen.Thus a rich pattern of fractional revivals, including some altogether new ones, are observed through this tool in both driven and un-driven situations.Finally we have elucidated various scenarios including cold atoms in magneto-optical traps where such a system can be experimentally realized along with the suggestions for future work in this specific domain
We calculate the quantum revival time for a wave packet initially well localized in a one-dimensional potential in the presence of an external periodic modulating field. The dependence of the revival time on various parameters of the driven system is shown analytically. As an example of an application of our approach, we compare the analytically obtained values of the revival time for various modulation strengths with the numerically computed ones in the case of a driven gravitational cavity. We show that they are in very good agreement.
Collapse and revivals in the Jaynes-Cummings model are studied within the context of the Mollow transformation for a single-mode coherent-state cavity field. The Mollow-transformed Jaynes-Cummings Hamiltonian has two atom-field terms, one corresponding to a classical field and the other to a quantized field driving the atomic transition. As such it maps onto the complementary problem of an atom in an optical cavity, whose field is initially in the vacuum state, driven by an external classical field. Both problems have the same atomic-state dynamics. It is shown that the revivals can be associated with two distinct properties of the quantized field of the transformed Hamiltonian. Revivals occurring at even (odd) multiples of the revival time are correlated with field states that are close to the initial field state and for which the average energy in the field is a minimum (maximum). Using semiclassical dressed states, we are able to map the problem for the field states onto one involving two uncoupled oscillators driven by off-resonant fields, provided effects related to dispersion are neglected. Analytic expressions for the photon number distribution of the transformed cavity field, including dispersion, are obtained for the even revival times.
A distinctive signature of the granulated nature of the electromagnetic field is the revivals known to occur in the dynamics of a two-level atom interacting with a single-field mode (Jaynes-Cummings model). The development of high-Q single-mode cavities combined with progress in Rydberg atom spectroscopy has led to a possibility of verifying these predictions. Revival experiments using micromasers have been performed by Walther et al. Here the cavity mode is first allowed to reach a steady state, and then probe atoms are injected into the resonator. By measuring their state as they exit the cavity, one can infer the state of the field. We show that the micromaser experiences Jaynes-Cummingslike revivals when the pump parameter θ is varied. However, in contrast to the conventional Jaynes-Cummings situation, which considers initially coherent fields, the micromaser photon statistics are usually not Poissonian and depend sensitively on θ. The micromaser revivals cannot be explained by a semiclassical theory or linearized quantum fluctuations about the semiclassical solution. Rather, an exact quantum treatment, considering fully the granularity of the cavity mode, is required.